Noninvasive Monitoring of Hepatic Damage from Hepatitis C Virus Infection

Abstract

The mathematical model for the dynamics of the hepatitis C proposed in Avendaño et al. (2002), with four populations (healthy and unhealthy hepatocytes, the viral load of the hepatitis C virus, and T killer cells), is revised. Showing that the reduced model obtained by considering only the first three of these populations, known as basic model, has two possible equilibrium states: the uninfected one where viruses are not present in the individual, and the endemic one where viruses and infected cells are present. A threshold parameter (the basic reproductive virus number) is introduced, and in terms of it, the global stability of both two possible equilibrium states is established. Other central result consists in showing, by model numerical simulations, the feasibility of monitoring liver damage caused by HCV, avoiding unnecessary biopsies and the undesirable related inconveniences/imponderables to the patient; another result gives a mathematical modelling basis to recently developed techniques for the disease assessment based essentially on viral load measurements.

Problema de control para el modelo básico de la hepatitis C con tratamiento

“…El documento está organizado de la siguiente manera: En la sección 2 presentamos las ecuaciones del modelo estudiado por Alavez-Ramirez et al [1]. En las secciones 3 y 4 se incluye tratamiento al modelo y se formula el problema de control óptimo.…”